Self-Consistent Calculations of Quasiparticle States in Metals and Semiconductors

We solve the Dyson equation for the one-particle Green's function in a periodic solid self-consistently within the shielded-interaction (or $\mathrm{GW}$) approximation. The effect of self-consistency (propagator renormalization) is found to be substantial. We illustrate this finding via calculations of quasiparticle states in K and Si. In the case of Si we show that the current standard of ab initio quasiparticle theory, the $\mathrm{GW}$ self-energy diagram, fails to account for the observed value of the absolute band gap—if properly, i.e., self-consistently, evaluated.